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以中介数学系统为背景,为处理工程实践和科学研究中普遍存在的模糊现象提供一种度量逻辑真值程度的方法.在建立了谓词的ε标准度概念后,描述了对一般应用的数值区域与对应谓词的真值之间的关系;采用距离概念,并以对应谓词真值的数值区域的长度为基准,定义了距离比率函数及距离比率的特殊变换,并由此建立了一维情形下个体真值程度函数.又在提出关于n维情形的分支谓词、幂集逆映射和标准度向量概念后,描述了真值程度和函数、极值分支函数等n维情形的应用形式.应用示例表明:由于提出超态概念,所以理论上能把真值程度域从[0,1]拓宽到(-∞,+∞);真值程度函数的定义具有计算机可以处理的定量形式且具有客观性和普适性的特点.因此,真值程度的度量将在涉及模糊现象的领域得到有效的应用.
Based on the intermediated mathematical system, this paper provides a method to measure the true value of logic in engineering practice and the fuzzy phenomena existing in scientific research.After establishing the concept of ε-standard of predicate, And the true value of the corresponding predicate. Based on the concept of distance and the length of the numerical region corresponding to the true value of the predicate, a special transformation of the distance ratio function and the distance ratio is defined and a one-dimensional case is established Individual truth degree function.After the concept of branching predicate, power set inverse mapping and standard degree vector about n-dimensional situation is proposed, the application form of n-dimensional situation such as true degree and function, extreme value branch function is described. It is shown that the concept of degree of truth can theoretically broaden the degree of truth range from [0,1] to (-∞, + ∞). The definition of truth degree function has the form of computer-processible quantification and is objective And pervasiveness, the measure of the degree of truth will be effectively applied in the field involving fuzzy phenomena.